Related papers: Random Spanning Trees for Expanders, Sparsifiers, …
We study the behavior of Random Walk in Random Environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the ratios of resistances of neighboring edges…
This paper makes two main contributions: The first is the construction of a near-minimum spanning tree with constant average distortion. The second is a general equivalence theorem relating two refined notions of distortion: scaling…
Spanning trees are relevant to various aspects of networks. Generally, the number of spanning trees in a network can be obtained by computing a related determinant of the Laplacian matrix of the network. However, for a large generic…
Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a…
We introduce the concept of Random Sequential Renormalization (RSR) for arbitrary networks. RSR is a graph renormalization procedure that locally aggregates nodes to produce a coarse grained network. It is analogous to the (quasi-)parallel…
Sampling a network with a given probability distribution has been identified as a useful operation. In this paper we propose distributed algorithms for sampling networks, so that nodes are selected by a special node, called the…
Graphs in many applications, such as social networks and IoT, are inherently streaming, involving continuous additions and deletions of vertices and edges at high rates. Constructing random walks in a graph, i.e., sequences of vertices…
The aim of this paper is to develop a method for proving almost sure convergence in Gromov-Hausodorff-Prokhorov topology for a class of models of growing random graphs that generalises R\'emy's algorithm for binary trees. We describe the…
We present the analytical and numerical results of a random walk on the family of small-world graphs. The average access time shows a crossover from the regular to random behavior with increasing distance from the starting point of the…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
In 1989, Zehavi and Itai conjectured that every $k$-connected graph contains $k$ independent spanning trees rooted at any prescribed vertex $r$. That is, for each vertex $v$, the unique $r$-$v$ paths within these $k$ spanning trees are…
We study the asymptotic behavior of four statistics associated with subtrees of complete graphs: the uniform probability $p_n$ that a random subtree is a spanning tree of $K_n$, the weighted probability $q_n$ (where the probability a…
We show that the geometry of minimum spanning trees (MST) on random graphs is universal. Due to this geometric universality, we are able to characterise the energy of MST using a scaling distribution ($P(\epsilon)$) found using uniform…
Spanning trees are an important quantity characterizing the reliability of a network, however, explicitly determining the number of spanning trees in networks is a theoretical challenge. In this paper, we study the number of spanning trees…
We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new…
Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with…
We introduce and study the {\em orderly spanning trees} of plane graphs. This algorithmic tool generalizes {\em canonical orderings}, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning…
We present a quantum algorithm for sampling random spanning trees from a weighted graph in $\widetilde{O}(\sqrt{mn})$ time, where $n$ and $m$ denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for…
Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…
We focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. We first present a fast sublinear…